Deep water pathways in the North Pacific Ocean revealed by Lagrangian particle tracking

Lagrangian particle tracking experiments are conducted to investigate the pathways of deep water in the North Pacific Ocean. The flow field is taken from a state-of-the-art deep circulation simulation. An unprecedented number of particles are tracked to quantify the volume transport and residence time. Half of the North Pacific deep water returns to the Southern Ocean, and its principal pathway is along the western boundary current in the Southwest Pacific Basin in the deep layer. About 30% is exported to the Indian Ocean after upwelling to the shallow layer in the western North Pacific Ocean. The rest is transported to the Arctic Ocean through the Bering Strait or evaporates within the Pacific Ocean. Upwelling of deep water is confined in the western North Pacific Ocean owing to the strong vertical mixing. The mean residence time of deep water in the North Pacific Ocean is estimated to be several hundred years, which is consistent with the observed radiocarbon distribution.

. Several observation-based studies 2,5,9 assumed that all (~ 10 Sv) of the Pacific deep water returns to the Southern Ocean in the deep layer. On the other hand, Talley 3 estimated about 9, 4, and 1 Sv of the Pacific deep water originated from the Southern Ocean are exported to the Southern, Indian, and Arctic Oceans, respectively. Our result is qualitatively consistent with this estimate 3 although the modeled export to the Southern and Indian Oceans is smaller. The modeled export to the Arctic Ocean is a bit larger than the observational estimate 20 of the net volume transport through the Bering Strait (~ 0.8 Sv). The residence time (seawater age) of the deep Pacific water is equivalent to the time required for particles to reach other basins. Its statistics are summarized in Table 1. The mean required time to reach the Southern, Indian, and Arctic Oceans and the atmosphere (evaporation) is 533, 627, 728, and 804 years, respectively. The median time is shorter than the mean time by about 100 years for each destination, and the mode time is even shorter because of the right-skewed frequency distribution in the arrival time (Fig. 2b). Note that the "mode time" means the year when the number of particles reaching each destination is largest. The residence time of particles is less than 1000 years and is consistent with an observation-based estimate of water age in the deep Pacific Ocean 21 .
Main pathway. The main pathways, defined in terms of particle tracking, are the routes where a large number of particles pass through. Therefore, the main pathways are visualized by superimposing the trajectories of the particles (left panels in Figs. 3 and 4). To identify the shortest pathways, the trajectories of the earliest 10% of the particles that leave the Pacific Ocean are extracted for each destination together with the horizontal positions where these particles first cross the depths dividing the bottom, deep, intermediate, and shallow layers ("ascending points" hereafter) (Fig. 3).
Most of the particles reaching the Southern Ocean ascend near the Samoan Passage (e.g., Melanesian Basin) and are transported southward in the Southwest Pacific Basin without crossing the equator ( Fig. 3a and b). Some   Fig. 3a and b), which corresponds to the Tasman leakage 22 . Except for the shallow layer (< 500 m depth), a majority of particles reaching the Indian Ocean through the Indonesian Archipelago are transported in the western North Pacific Ocean, not in the east (Fig. 3c). The particles are transported in the Central Pacific Basin or the Melanesian Basin in the bottom layer, then join and ascend to the deep layer at the Izu-Ogasawara Ridge where turbulent vertical mixing is strong ( Fig. 3c and d). These particles ascend to the intermediate layer (500-1000 m depth) at the Luzon Strait (around 20°N, 120°E) and around the Ryukyu Islands and are transported to the Indonesian Archipelago ( Fig. 3c and d). The particles on the secondary pathway ascend to the deep layer in the Melanesian Basin and to the intermediate layer in the Solomon Sea or North/South Fiji Basin and reach the Indonesian Archipelago ( Fig. 3c and d).
The trajectories and ascending points of most of the particles reaching the Arctic Ocean are similar to those reaching the Indian Ocean in the deep and bottom layers ( Fig. 3e and f). In the shallow and intermediate layers, www.nature.com/scientificreports/ the particles are transported by the Kuroshio, its extension, and the North Pacific subarctic gyre, and reach the Bering Strait (Fig. 3e). The particles on the secondary pathway ascend around the Kuril and Aleutian Islands, where the turbulent vertical mixing is locally enhanced, from the bottom layer to the shallow layer (Fig. 3f). The trajectories and ascending points of particles evaporating within the Pacific Ocean are similar to those reaching the Arctic Ocean below the intermediate layer (> 1000 m depth). Evaporation of particles mainly takes place in the equatorial Pacific Ocean (figure not shown). The particles are transported to the low-latitude region by the North Pacific subtropical gyre and the Equatorial Counter Current in the shallow layer ( Fig. 3g and h).
The particles which reside longer in the North Pacific Ocean follow different pathways. Here, the trajectories are extracted for the particles with around the median residence time (between 45 and 55 percentiles) in the Pacific Ocean. (Fig. 4). The returning routes in the deep layer to the Southern Ocean are localized in the western part of the Southwest Pacific Basin for the short-staying particles ( Fig. 3a and b), while the routes of the medium-term-staying particles are distributed over the whole Pacific Ocean ( Fig. 4a and b). In summary, the main pathway of particles transported to the Southern Ocean in the deep layer is found in the western part of the Southwest Pacific Basin, and the secondary is found in the Southeast Pacific Basin. This main pathway differs from previous suggestions inferred from the distribution of temperature and salinity: along the eastern edge of the Southwest Pacific Basin 2 or eastern boundary of the Pacific Ocean 9 .
The pathway of the short-staying particles that reach the Indian Ocean is localized in the western Pacific Ocean (Fig. 3c), while the pathway of medium-term staying particles spreads over the Pacific Ocean (Fig. 4c). The ascending points are also distributed in the whole Pacific Ocean in the bottom and deep layers (Fig. 4d). These features of the pathway are similar for the particles reaching the Arctic Ocean and the atmosphere (figure not shown).
Even when the trajectories are randomly selected from all particles, the main pathways are little influenced compared with the case of medium-term staying particles ( Figure S1). They are, however, obscured because the slower particles are more likely to be scattered over the whole deep Pacific Ocean.
Dependency on flow field. Because the northward transport of bottom water at the Samoan Passage (and its adjacent passages) in the case 1D is larger than that in the case 3D, the number of released particles is also larger in the case 1D (Fig. 5a and c). Almost all the particles leave the Pacific Ocean after 3000 years (Table 2; Fig. 2c). The ratio of the particles reaching the Southern Ocean (57.9%) is larger than that in the case 3D (46.5%), while the ratio of particles reaching the Indian (19.1%) and Arctic Oceans (2.2%) are smaller (Tables 1 and 2). The residence time of the particles reaching the Southern Ocean is smaller than that in the case 3D, while that for the Indian and Arctic Oceans is larger (Tables 1 and 2, and Fig. 2b and d). This behavior of the particles in the case 1D is associated with the small vertical mixing in the deep layer.
The ascending points of particles are localized around the ridges, seamounts, and boundaries in the case 3D, while they are homogeneously distributed in horizontal in the case 1D as a result of the horizontally uniform vertical diffusivity (Fig. 6). The strong vertical mixing localized in the western North Pacific Ocean in the case 3D causes the efficient ascending of particles and short required time to reach the Indian and Arctic Oceans (Fig. 2d, Tables 1).   www.nature.com/scientificreports/ Pacific Ocean is not consistent with the conventional understanding of the time scale of the deep Pacific Ocean circulation, which was considered to be several thousand years 23,24 , but is consistent with an estimate based on radiocarbon 21 . The principal pathway to the Southern Ocean in the deep layer is along the western boundary of the Southwest Pacific Basin, which is different from what was suggested by Kawabe and Fujio 9 (along the eastern boundary of the Pacific Ocean). It should be noted that the fate of flow into the North Pacific Ocean in the deep layer, whose existence is suggested by Kawabe and Fujino 9 , is not treated in this study. An insufficient number of particles may prevent isotropic diffusion representation and bias the pathways. To verify whether the number of particles tracked in this study is sufficient to estimate the volume transport, we divide the particles into 11 groups and performed the same analysis. As a result, the spread of the estimate is within 1% (e.g., 3.482 ~ 3.505 Sv for volume transport to the Southern Ocean in the case 3D). The horizontal diffusivity itself has uncertainty. We conducted the particle tracking with halved or doubled horizontal diffusivity. The mean residence time is longer/shorter by about 20% for the halved/doubled horizontal diffusivity (Table S1). This result suggests the nonnegligible sensitivity of the deep water age to horizontal mixing. The reality of horizontal mixing and its influence on the deep Pacific Ocean circulation is left to be investigated.
Coarse-resolution models, as utilized in this study, cannot adequately represent western boundary currents in the shallow layer (such as the Kuroshio and the Oyashio) and the intermediate layer circulation. Therefore, it is necessary to use a velocity field obtained by an eddy-resolving ocean model to estimate the pathways in the shallow and intermediate layers more accurately. There are several studies applying particle tracking to eddyresolving models 25,26 , but none for long time scales as in this study. There is difficulty arising from not only the huge size of computation and data to handle but also how to properly consider interannual variability associated with oceanic internal variations. We are currently tackling this problem.

Methods
Velocity and diffusivity fields. As the velocity and diffusivity fields for particle tracking, we utilize the results of an ocean general circulation model experiment conducted by the previous study (experiment CTRL of Kawasaki et al. 18 ). The horizontal resolution of the model is 1 degree. We applied constant diffusivity of 1000 m 2 s -1 for the horizontal unresolved-eddy-induced mixing. In this experiment, the three-dimensional distribution of vertical turbulent mixing, to which the deep Pacific Ocean circulation is highly sensitive, is given based on the results of a high-resolution tide model 27 and theoretical and observational studies [28][29][30][31] . This circulation field and the particle tracking using this field are named the "case 3D". For comparison purposes, the velocity and diffusivity fields calculated by prescribing an empirical distribution of vertical diffusivity (Case III of Tsujino et al. 16 ), which is horizontally uniform and varies only in vertical, in the same ocean model are also used for particle tracking (case 1D).
Since the employed circulation field does not explicitly resolve mesoscale eddies and further smaller features and is driven by monthly mean sea surface boundary conditions, both high-frequency and interannual variabilities of ocean currents are not simulated. Therefore, the climatological (30-year mean) monthly mean velocity and diffusion fields are utilized for particle tracking. The bolus velocity associated with the thickness diffusion parameterization 32 applied in the model is added to the velocity field. Note that the bolus velocity is small and does not have a significant impact on particle tracking due to the relatively flat isopycnals in the deep Pacific Ocean.
The northward transport of deep water at the Samoan Passage and its adjacent pathways (~ 10°S) in the bottom layer (> 3500 m depth) is 7.52 and 11.2 Sv (Fig. 5a and c) in the cases 3D and 1D, respectively. Although this is smaller than the estimate from mooring measurements 6,8,33 (~ 9-10 Sv below 4000 m depth), the simulated radiocarbon distribution is quantitatively and qualitatively consistent with the observation in the deep Pacific Ocean in the case 3D ( Fig. 5b and e). Because the radiocarbon is an indicator of how long it has taken since seawater is isolated from contact with the atmosphere, the qualitative and quantitative consistency means the validity of the structure and strength of the deep Pacific Ocean circulation. In the case 1D, the northward volume transport is larger than the observational estimation, and the calculated radiocarbon is also too high, indicating too short residence time of deep water in the North Pacific Ocean (Fig. 5d and e). Note that the northward volume transport at the Wake-Island Passage (18°N, 169°E) and its western passages below 3500 m depth is 3.04 and 3.35 Sv in the cases 3D and 1D, respectively, which are smaller than observed transport (a little more than 3.6 Sv below 3670 m) 7 . www.nature.com/scientificreports/ Particle tracking. The Lagrangian particle tracking system used in the present study is the same as in Nakano et al. 25 , which is a part of an ocean modeling system kinaco (source code available via http:// lmr. aori.utokyo. ac. jp/ feog/ ymatsu/ kinaco. git). The trajectory of each particle is integrated by the fourth-order Runge-Kutta method using the combination of the bilinear-interpolated velocity field (sum of the resolved current and the parameterized bolus velocity) and the turbulent mixing represented by normal-distributed random displacement whose standard deviation corresponds to the unresolved-eddy-induced diffusivity. Particles are released from the Samoan Passage and its adjacent pathways below 3500 m depth where the bottom water heading to the North Pacific Ocean from the Southern Ocean always passes due to the topographic constraint (Fig. 7). One particle is released every time the northward volume transport reaches 1 × 10 8 m 3 on the prescribed section in the passage (shown by a red line in Fig. 7). By so doing, a quantitative evaluation of the pathway is feasible by tracking particles.
Particles are released only for the first year. The total numbers of released particles for the cases 3D and 1D are 2,342,025 and 3,475,625, which correspond to the deep water volume transport of 7.53 and 11.2 Sv, respectively. Each particle stores an index for extinction which is initially zero. It increases by the rate of evaporation at the sea surface when the particle resides in the top-most layer of the model (2 m thick). When the accumulated value for any particle exceeds half of the top-most layer thickness (1 m), the particle is removed by considering the volume of water represented by the particle has evaporated out.
By tracking these particles, it is possible to determine the pathways of the deep water that has passed through the Samoan Passage (and its adjacent passages). The volume transport for each pathway is also determined by counting the number of particles on the pathway. The volume transport thus calculated at a certain location is different from the actual volume transport at that location, and their ratio indicates the percentage contribution of the water coming through the Samoan Passage to the total volume transport.
It should be noted that each particle in the current method does not correspond to a water mass in the conventional sense as it does not experience mixing of water (or transformation of the water mass). Each particle